Step 1: Concept
$O^{2-}$ and $N^{3-}$ are isoelectronic species (same number of electrons).
Step 2: Analysis
For isoelectronic ions, as the negative charge increases, the ionic radius increases.
Step 3: Conclusion
The electrons are held less tightly by the nucleus in $N^{3-}$, making its radius greater than $O^{2-}$.
Final Answer: (B)